Conventionally, automatic idling-stop systems, which automatically stop idling when a predetermined condition is satisfied, have been developed for the purposes of improvement of fuel efficiency of an automobile, reduction of an environmental load, and the like. Among the automatic idling-stop systems, the one using a starter requires only a small change in a system of a vehicle, and therefore is low in cost. On the other hand, however, there is a problem in that meshing engagement cannot be achieved until the engine is completely stopped.
In order to cope with the problem described above, there exists an idling-stop system which rotates a starter motor during cut-off of a fuel to an engine and then controls energization of the starter motor to rotate the starter motor by inertia so as to connect the starter motor to the engine while both the engine and the starter motor are rotating by inertia (see Patent Literature 1, for example).
Moreover, there also exists an engine automatic stop and restart device, which predicts a future ring-gear rpm to predict time at which a pinion rpm comes into synchronization with the future ring-gear rpm and controls pinion-gear pushing timing or pushing speed so that the pinion rpm and the ring gear rpm come into synchronization at the predicted time (see Patent Literature 2, for example).